There is no contexual meaning seen for the underlined word in the first sentence.
wrapped <---> swathed (second sentence)
- Wrapped around his forehead <---> Swathed around his forehead...
The definition of swathe is to wrap in many fabrics.
occupied <---> engaged (third sentence)
- As you are occupied... <---> As you are engaged...
Engaged can mean to be busy or occupied.
allowed <---> suffered (fourth sentence)
- I allowed him to hurry me<-->...I suffered him to hurry me...
An archaic meaning of suffered can mean to allow someone to do something.